Reversed Field Pinch Approach to Magnetic Fusion S. Ortolani, Padova (Istituto Gas Ionizzati del C.N.R. Associazione Euratom-CNR)

The process whereby a current chan­ Table 1 — RFP devices in operation, under construction and contemplated nel contracts under the influence of the magnetic field generated by the current ETA BETA II TPE-IR (M) ZT-40 (M) HBTX-IA OHTE RFX REACTOR (Padova, Italy) (Sakura-Mura, (Los Alamos, (Culham, UK) (General Atomic, (Padova, Italy) itself, is known as the "pinch effect" and Japan) USA) USA) it was first studied by Bennett in 1934. It Torus Major Radius, m 0.65 0.5 1.14 0.8 1.24 2 4.0 13 was also the first to be used experimen­ Torus Minor Radius, m 0.125 0.09 0.2 0.26 0.19 0.5 0.75 1.5 tally (by Cousins and Ware in 1951) to Plasma Current, MA 0.25 0.15 0.6 0.5 0.5 2 18.5 20 confine plasma in a magnetic field in First Operation 1979 1980 1981 1981 1981 1988 toroidal geometry. Indeed, during the 1950s pinches, both linear and toroidal, The first large toroidal device in which required for thermonuclear fusion (T  were the most widely studied systems RFP configurations were studied was 10 keV, E  1 s) and to those achieved in fusion research. ZETA (UK), which operated during the in present day tokamaks (T  5 keV, E The main observation from these 1960s, where improved stability and = 0.1 s), but there is now a firmer scien­ early experiments was that the plasma confinement were observed when the tific basis for extending RFP research to was macroscopically unstable because plasma spontaneously generated a re­ bigger systems and higher currents. of the fast growing magnetohydrodyna- versed toroidal field in the outer region. While the scientific feasibility of con­ mic (MHD) instabilities which destroyed The importance of the reversed field trolled thermonuclear fusion will proba­ the symmetry of the plasma column and configuration both experimentally and bly be demonstrated in the tokamak led to wall contact. theoretically was better understood dur­ configurations 1), it is now recognized The addition of a longitudinal magne­ ing the 1970s. A number of small toroi­ that alternative schemes such as Mirrors tic field (Bz in cylindrical geometry, Fig. dal devices were built and operated in 2), Stellarators 3) and the RFP may offer 1; Bf in toroidal geometry, Fig. 2) was that period (UK, USA, Italy, Japan) and more advantageous solutions for nu­ suggested by theoretical studies and led many of the theoretical predictions of clear fusion reactors. to experiments on the so called "stabiliz­ the MHD theory were experimentally The RFP like the tokamak is a toroidal ed pinch" configuration (with Bf  B ). confirmed. axisymmetric configuration but, where­ Although the macroscopic stability of During the same period, a major ad­ as in the tokamak the plasma current is the plasma improved, residual instabi­ vance in our theoretical understanding limited by stability requirements: lities and fluctuations caused poor of toroidal pinch discharges was made. / < 2πa2BfI o plasma confinement. It was realized that the most important the RFP can use high currents and One possible way of overcoming the property of the RFP is that the magnetic powerful ohmic heating to produce rela­ pinch instabilities, proposed during the configuration is a minimum energy state tively high-β ( 10%) plasmas without 1960s was the tokamak configuration in to which, under certain conditions, the the need for either very high toroidal which a large toroidal field is applied so plasma can spontaneously relax. This fields or powerful auxiliary heating that Bf/B is larger than the ratio of basic property was first discussed in methods. Furthermore it is now clear major to minor torus radius, R/a, and the 1974 by J.B. Taylor who revived Wolt- that although the RFP originally was most dangerous helical deformations of jer's astrophysical theorem on force-free thought to be intrinsically a pulsed the plasma cannot form because of the magnetic fields and extended it to labo­ device, the same processes which can periodicity conditions. At about the ratory plasma discharges. It is in practice lead to the formation of the configura­ same time a second approach appeared : this property of minimum energy state tion can also maintain it and give quasi the Reversed Field Pinch (RFP) in which which gives to the RFP its favourable steady state operation. Bf  B but the toroidal field compo­ stability characteristics and makes it of nent in the outer region has the opposite particular interest among toroidal sys­ Equilibrium sign to that on the magnetic axis, thus tems for magnetic confinement. In the RFP the distributions of both the creating a high shear of the field lines A new generation of experiments has poloidal and toroidal field components and forming a stable radial distribution become operational during the last seve­ of the magnetic field. ral years (see Table 1) and it is now gene­ Fig. 1 —Cylindrical geometry. rally observed that the RFP configura­ Fig. 2 — Toroidal geometry. tion can confine relatively high β plas­ mas, heated by ohmic heating only, with moderate magnetic fields, Bf  B < 1T. (P is the ratio between the plasma kinetic pressure and the magnetic field pressure. For a fusion reactor to be eco­ nomic it should be greater than about 10%.) The temperatures and confinement times achieved (T < 0.6 keV, E < 0.3 ms) are still modest compared to those 5 are mostly determined by currents flow­ sion and the hoop force of the toroidal ing in the plasma, the total current densi­ current. Equilibrium can be established ty being almost parallel to the magnetic through the influence of a conducting field. For an ideal equilibrium in toroidal wall or a vertical field. If the plasma is geometry (Fig. 2), the magnetic sur­ surrounded by a perfectly conducting faces are nested toroidal surfaces (Fig. shell, the equilibrium is achieved when 3) on which the magnetic field lines are the plasma shifts far enough that the in­ helically wound with a pitch length (for a creased magnetic pressure, due to the Fig. 3 — Toroidal magnetic flux surfaces. circular cross section of the magnetic compression of poloidal flux, balances surfaces) : the outward force. In the RFP, because dients substantially smaller than the cri­ P = rBf/B = qR =  f RI2π β is small and a/R can be small, only a tical value set by the Suydam's criterion. where  f is the change in toroidal angle small outward shift (typically a few per­ of a magnetic line after traversing one cent of the plasma minor radius) is ne­ Minimum Energy State poloidal circuit and q represents the cessary to compress sufficient flux for Although stable high β equilibrium number of times the field line encircles toroidal equilibrium. profiles exist theoretically, they are dif­ the major axis in making one turn of the ficult to achieve experimentally by direct minor axis. It is worth noting that in a programming of the toroidal and poloidal tokamak, q > 1 (typically  R/a) and in a Stability electrical circuits. The main reasons are RFP, q < 1 (typically < a/R). Moreover in Obviously a plasma confined by a technological : for a full control of the the RFP, the helical field lines have dif­ magnetic field away from the cold first profiles, programming on a short (MHD) ferent pitches on the various magnetic wall cannot be in the lowest energy state timescale implying high voltages, would surfaces (i.e. q is a function of minor as that would be characterized by ther­ be required. However these RFP confi­ radius) and the direction in the outer mal equilibrium. Confinement studies gurations have been demonstrated by region is opposite to that in the central aim then to find dynamical equilibria J.B. Taylor to be minimum energy states part of the toroidal plasma; this is illus­ with inhomogeneous plasma, and ma­ to which, under certain conditions, the trated in Fig. 4. gnetic field spatial distributions which plasma can spontaneously relax. can be stable for times longer than the RFPs can have a large aspect ratio R/a For a plasma surrounded by a perfect­ and therefore the radial pressure balance energy and particle confinement time. ly conducting wall, the minimum energy The spatial gradients of the plasma in the poloidal plane can be described in magnetic configuration is described by the simpler geometry of a straight kinetic pressure and the current density the solutions of the equation: cylinder (Fig. 1). In this case the equili­ distribution are the two main sources of  x B = µB brium equation for the poloidal beta macroscopic instabilities. with p constant throughout the plasma. which is defined as: The stability for localised pressure This configuration corresponds however driven modes can be discussed on the to a large parallel current density flowing basis of Suydam's criterion. This states out to the wall. Also the z-component of that in cylindrical geometry, stability is the current density should substantially where p is the plasma pressure is : obtained when reverse in the outer region. Experimentally, the magnetic field dis­ tribution in the central region of the The two parameters F and  which plasma is of the form given by Taylor's characterize the pinch are defined as : and shows that the destabilizing effect theory, but not in the outer region where F = Bz(a) and  = B (a)/. of the negative pressure gradient can be there is little or no current because the These equations reduce with βf = 1 to compensated by a sufficiently large plasma temperature near the wall is the Bennett equilibrium equation: shear (dq/dr) in the magnetic field. usually low. Fig. 5 presents profiles typi­ It is also evident that if dq/dr = 0 fying experimental findings for µ varying when dp/dr < 0, the Suydam criterion as µ = (2 O/a) (1 - (r/a)4} with  o = cannot be satisfied. This can be avoided 1.6. For this radial profile, the unrealistic where N is the total number of particles when there is a vacuum region separa­ features of the BFM are removed and per unit length and (Te + Ti) is averaged ting the plasma from the conducting one arrives at the conclusion that the ex­ over all these particles. wall if there is a reversal of Bz. The rea­ perimental distributions are near mini­ In the case of the tokamak with Bz son is that in vacuum, q = q(a) (r/a)2, mum energy states. almost uniform and so F2  1, equilibria where a is the radius of the plasma, with β  1 are possible, whereas in the whereas in the central region of the RFP, RFP, characterized by F2  0 and Fig. 4 — Magnetic field lines on an inner and q decreases with r, implying a minimum an outer magnetic surface of a RFP configu­ l2 > 1, the pressure ba­ in the radial profile unless q changes sign ration. lance condition requires  > 1 and in ge­ in the outer region. This is achieved by neral β < (1-1/  2). The total β is related the reversal of the toroidal field which ef­ PLASMA to the poloidal beta by : fectively maintains the shear high in the outer portion of the configuration. A detailed study of the MHD stability so that in the tokamak β << β , where­ for pressure driven and current driven as in the RFP they are equal within a fac­ modes shows that RFP profiles comple­ tor of two. tely stable to both are possible with The problem of toroidal equilibrium average total beta as high as 20%. How­ consists of compensating the outward ever it should be noted that if the finite force arising from the gas kinetic expan­ resistivity of the plasma is taken into ac­ count, instability sets in at pressure gra- 6 It is very important to notice that the relaxation to this near minimum energy distribution is a continuous process by which the field configuration can be maintained for times longer than the characteristic resistive diffusion time. In fact in a stable plasma described by clas­ sical MHD transport, a steady-state RFP could not be maintained. MHD turbu­ lence or instabilities are required to drive the plasma currents which generate the field distribution. By analogy to the as- trophysical and geophysical case, this is sometimes referred to as the dynamo process. Present and Future Experiments Recently, there has been much new information from five intermediate sized RFP machines (a = 9-26 cm) at currents of a few hundred kA. In Table 1 are listed some of the main parameters of the va­ rious experiments along with the para­ meters of the RFX experiment and of two possible reactor units. In present ex­ periments, the plasma parameters are: Te is of the order of a few hundred eV (maximum 0.6 keV), ne of the order of 1013-1014 cm-3, β  0.1, with typical pulse lengths of  10 ms, during which time the magnetic field configuration is Fig. 5 — Comparison between typical RFP profiles (solid lines) and the theoretical BFM sustained by the "dynamo" mechanism. profiles (dashed lines). The fluctuation level ( B/B  1%) is relatively low. The energy confinement Such a dependence is similar to that of ment deteriorates. If the RFP will main­ times lie in the range 0.03-0.3 ms. the magnetic field diffusion time and to tain the presently achieved values of P in One of the most important observa­ that of the classical ion heat conduction a plasma with parameters closer to tions is the dependence of the plasma across the magnetic field due to Cou­ those of thermonuclear fusion, it will parameters on density. There exists a lomb collisions. constitute a major alternative for a prac­ high filling density limit which may be This β = constant scaling of the tical fusion reactor. compared to that in tokamaks and oc­ energy confinement time is also consis­ Hence the RFX experiment which curs at about the same value of the ratio tent with the concept that the basic received construction approval last Oc­ of plasma current to plasma line density, relaxation process, which maintains the tober. It is a large RFP with a toroidal l/N  10-14 A m, beyond which the dis­ RFP configuration near to the minimum vessel of major and minor radii of 2 m charge is cold, resistive and radiation energy state, occurs through resistive and 0.5 m respectively, designed to ope­ cooled because low-Z impurities are not unstable modes whose characteristic rate with 2 MA toroidal plasma current. burnt through. In general, after an initial time scale is the resistive diffusion time It is being built at Padova and has been rise due to ionization, the density falls  R  a2Te3/2· approved by the European Communities during the pulse, sometimes reaching an A comparison of ohmically heated for priority action within the European approximately constant value; in many tokamaks and pinches shows that small fusion programme qualifying thereby for experiments a large fraction of the initial low current machines yield substantially preferential support. It represents a sub­ density is lost. Essentially, although gas higher values of temperature and energy stantial step in RFP research. Its objec­ puffing (which is difficult in these expe­ confinement time in the tokamak mode, tive is to demonstrate the possibility of riments) and toroidal field control in­ but with a much lower value of β. Extra­ producing temperatures and confine­ fluences the density to some extent, it polating to larger experiments, with cur­ ment times much closer to those requi­ cannot be controlled externally. rents in the MA range, gives tempera­ red in a reactor and to compare the The highest temperatures have so far tures and energy confinement times results with those from present day usually been reached at low density; to which, with β  0.1, will be similar in large tokamaks. The expected plasma reach high temperatures ( 1 keV) at the RFP and in ohmically heated toka­ parameters in RFX are T < 1 keV, n  high densities (  1014 cm _3) currents in maks. However in the pinch these 1014 cm -3, E  10 ms, β  10%. the MA range are required. should be obtained with lower toroidal RFP experiments obtain typically va­ fields and larger values of total β than In Conclusion lues of β  0.1 fairly independently of would be obtainable in the tokamak by The RFP's high beta capability, when the current in a range from 50 to  500 ohmic heating. combined with favourable topological kA. This corresponds approximately to a In general, low β tokamaks provide features and the possibility for ohmic linear increase of the temperature with good plasma confinement, but when heating to ignition, may offer valuable current and a scaling of the energy con­ their β becomes comparable to that of options in fusion reactor development finement time of the form E  a2Tee 3/2. an ohmically heated RFP the confine­ as they can lead to a less complex, less 7 expensive, reactor scheme than the tokamak or stellarator with the possibili­ The Seventh European Regional ty of a smaller sized unit. At the values of β which are in prin­ Astronomy Meeting ciple possible in the RFP, the magnetic field will be relatively small and since the B field decreases outward with plasma radius as 1/r the magnetic forces on ex­ ternal conductors can be quite modest. The Seventh European Regional As­ 400 participants, with the presentation Since the aspect ratio is not restricted by tronomy Meeting, organized by the Eu­ of about 240 contributions. The invited stability considerations, an open struc­ ropean Physical Society and the Interna­ papers will be published by the Societa ture with R/a  5-10 can be used; this tional Astronomical Union, took place in Astronomica Italiana (Largo E. Fermi, 5, further eases the problems of magnetic Florence from December 12 - 16, 1983. I-50125 Firenze). forces and is advantageous for a reactor. It was cosponsored by the Italian Minis­ During the last two days of the mee­ If ignition by ohmic heating alone is try of Education, Arcetri Astrophysical ting, three full-day specialized sessions possible, the complexity and cost of ad­ Observatory, the University of Florence, were organized on the following sub­ ditional heating will be avoided, which is and the Italian Astronomical Society. jects: a major simplification. The opening ceremony was quite spec­ — the NL-UK-USA Infrared Astro­ Although as presently envisaged the tacular since it was held in the old palace nomy Satellite, IRAS; RFP reactor would be pulsed, it is now "Palazzo della Signoria", with trumpet — the European X-ray Satellite, clear that the magnetic field distribution players in Renaissance costumes behind EXOSAT ; is self-generating and this can lead to a the official table. — Atomic and Molecular Physics for The EPS and IAU are interested in pro­ Astronomy. quasi steady state operation. For full moting scientific exchange between as­ steady state operation, means must be found, as for all systems using transfor­ tronomers, astrophysicists and physi­ IRAS mer coupling, to drive the toroidal cur­ cists, the borders between their disci­ IRAS was launched on 25 January, rent continuously. Methods proposed plines often being difficult to define. One 1983, and ended its astronomical life on of the means of achieving this goal is to for the tokamak using neutral beam or 22 November, 1983 when its coolant high frequency driven currents in prin­ organize regular meetings on the Euro­ ran out, but in the course of the first six ciple might apply in a pinch, and will be pean level: these meetings should also months, the spacecraft was able to view provide the young scientists with an op­ the entire celestial sphere. The cooled investigated and tested at a more advan­ portunity to meet the more established, ced stage of pinch development. 22.4 in telescope mapped the area in and to publicize their own work. bands centred around 12, 25, 60 and The IAU has been organizing Euro­ 100 µm and made more detailed obser­ REFERENCES pean Regional Meetings for several vations of several targets. There has 1. Gibson A., Europhysics News 14 (1983) 4. years now; been very little release of scientific data 2. Baldwin D.E., Europhysics News 12 (1981) — 1972, Athens: "Solar Activity and so far: first accounts are to appear in a 8/9. Related Interplanetary and Terrestrial series of papers in Astrophysical Journal 3. Wobig H., Europhysics News 13 (1982) Phenomena" — "Stars and the Milky Letters (March 1984), and a catalogue is 8/9. Way System" — "Galaxies and Relati­ scheduled for August-September 1984 FURTHER READING vistic Astrophysics". (with positions and other information on — 1974, Trieste: "Stars and Stellar more than 200000 far-infrared sour­ — for early pinch work see Glasstone S., Evolution". Lovberg R.H., Controlled Thermonuclear ces). Reactions (D. Van Nostrand, Princeton, N.J.) — 1975, Tbilisi: "Stars and Galaxies The specialized session organized in 1960; from Observational Points of View”. Florence gave the participants the occa­ — for a summary of the results up to 1978, — 1978, Uppsala: "Stars and Star sion to listen to a series of talks which in­ see Ortolani S., Reversed Field Pinch Con­ Systems". cluded several on comets and fast mov­ figuration, Nuclear Fusion 19 (1978) 535; — 1980, Liège: "Variability in Stars ing objects, the "minor planet" or burn­ — for a general review of the RFP research and Galaxies". ed out comet 1983 TB, a solar system up to 1979, see Bodin H.A.B. and Newton — 1982, Dubrovnik: "Sun and Plane­ dust ring, the "infrared cirrus" clouds A.A., Reversed Field Pinch Research, Nu­ tary System". (very cold dust at  35°K, present even clear Fusion 20 (1980) 1255; The first six meetings were topical i.e. in the direction of the galactic poles), — for more updated reviews, see Bodin H.A.B. and Ortolani S., the Status of RFP Ex­ essentially devoted to one (sometimes galactic cold dust (part of the "missing periments, University of Padova Report very broad) subject whereas the se­ mass"?), stars with dust shells (ring of UPee 82/09 (1982); venth showed the result of a tighter col­ solid particles around Vega, older clouds Dreicer H., Topics in Reversed Field Pinch laboration between the EPS and the IAU, at larger distances around Betelgeuse), Physics, Physica Scripta T2/2 (1982) 435; in the following sense: talks in any the Crab Nebula, sources in Molecular — for reports on progress in the major expe­ astrophysical discipline were accepted, Clouds, the Andromeda Galaxy M31, in­ riments, see the proceedings of the biennal and parallel sessions as well as invited frared galaxies (a huge number of them IAEA Conferences on Plasma Physics and talks were organized on topics at the visible at the long wave bands), clusters Controlled Nuclear Fusion Research; frontier between astronomy and physics and quasars, and the intriguing blank — for a recent collection of papers on RFP and/or in areas where new develop­ theory and experiments see the proceedings fields (IR sources with presently no op­ of the Course and Workshop on Mirror ments in physics are important for astro- tical counterpart). After these presenta­ Based and Field Reversed Approaches to physical research. tions of IRAS results, it was very clear Magnetic Fusion, Varenna, Sept. 7-17 It is fair to say that this Seventh that the astronomical community was (1983), to be published by the Commission Regional Astronomy Meeting was a anxiously waiting for the release of the of the European Communities. great success since it attracted over first papers and of the catalogue since 8